Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections. 39 refs.

[1]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[2]  Clifford Ambrose Truesdell,et al.  Exact theory of stress and strain in rods and shells , 1957 .

[3]  A. Green.  The equilibrium of rods , 1959 .

[4]  B. D. Veubeke,et al.  A new variational principle for finite elastic displacements , 1972 .

[5]  E. Reissner,et al.  On One‐Dimensional Large‐Displacement Finite‐Strain Beam Theory , 1973 .

[6]  The Role of Saint Venant’s Solutions in Rod and Beam Theories , 1979 .

[7]  R. G. Muncaster.  Saint-Venant's problem in nonlinear elasticity: a study of cross sections , 1979 .

[8]  D. F. Parker.  An asymptotic analysis of large deflections and rotations of elastic rods , 1979 .

[9]  V. Berdichevskiĭ.  On the energy of an elastic rod , 1981 .

[10]  L. W. Rehfield,et al.  Toward a New Engineering Theory of Bending: Fundamentals , 1982 .

[11]  M. Borri,et al.  Anisotropic beam theory and applications , 1983 .

[12]  L. A. Starosel'skii,et al.  On the theory of curvilinear timoshenko-type rods , 1983 .

[13]  S. Atluri.  ALTERNATE STRESS AND CONJUGATE STRAIN MEASURES, AND MIXED VARIATIONAL FORMULATIONS INVOLVING RIGID ROTATIONS, FOR COMPUTATIONAL ANALYSES OF FINITELY DEFORMED SOLIDS, WITH APPLICATION TO PLATES AND SHELLS-I , 1984 .

[14]  R. Ogden.  Non-Linear Elastic Deformations , 1984 .

[15]  O. Bauchau.  A Beam Theory for Anisotropic Materials , 1985 .

[16]  Inderjit Chopra,et al.  Aeroelastic Stability Analysis of a Composite Rotor Blade , 1985 .

[17]  M. Borri,et al.  A large displacement formulation for anisotropic beam analysis , 1986 .

[18]  Lawrence W. Rehfield,et al.  Analysis, design and elastic tailoring of composite rotor blades , 1986 .

[19]  P. Friedmann,et al.  Structural dynamic modeling of advanced composite propellers by the finite element method , 1987 .

[20]  A. Stemple,et al.  A finite element model for composite beams with arbitrary cross-sectional warping , 1987 .

[21]  Dewey H. Hodges,et al.  Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor , 1987 .

[22]  Olivier A. Bauchau,et al.  Nonlinear Composite Beam Theory , 1988 .

[23]  Alan D. Stemple,et al.  Finite-Element Model for Composite Beams with Arbitrary Cross-Sectional Warping , 1988 .

[24]  Dewey H. Hodges,et al.  A Beam Theory for Large Global Rotation, Moderate Local Rotation, and Small Strain , 1988 .

[25]  Dewey H. Hodges,et al.  Nonlinear analysis of a cantilever beam , 1988 .

[26]  S. Atluri,et al.  On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams , 1988 .

[27]  John Dugundji,et al.  Experiments and analysis for structurally coupled composite blades under large deflections. II - Dynamic behavior , 1989 .

[28]  A. Atilgan.  Towards a unified analysis methodology for composite rotor blades , 1989 .

[29]  Dewey H. Hodges,et al.  Review of composite rotor blade modeling , 1990 .

[30]  Dewey H. Hodges,et al.  Nonclassical Behavior of Thin-Walled Composite Beams with Closed Cross Sections , 1990 .

[31]  D. Hodges.  A mixed variational formulation based on exact intrinsic equations for dynamics of moving beams , 1990 .

[32]  Mark V. Fulton,et al.  Free-Vibration Analysis of Composite Beams , 1991 .

[33]  Carlos E. S. Cesnik,et al.  On a simplified strain energy function for geometrically nonlinear behaviour of anisotropic beams , 1991 .

[34]  Marco Borri,et al.  Composite beam analysis linear analysis of naturally curved and twisted anisotropic beams , 1992 .